Approximate multiscale stochastic stress analysis of randomly arranged unidirectional fiber reinforced composites by successive local approximation with hexagonal array model

Abstract

This paper discusses an approximate multiscale stochastic stress analysis of a randomly arranged unidirectional fiber reinforced composite plate under the transverse tensile loading. The multiscale stochastic stress analysis is desired for quantitative apparent strength evaluation of composites with random microstructure, and an efficient method has been attractive in terms of computational efficiency. In particular, since huge numbers of fibers are included in an actual composite structure, accurate and efficient estimation of microscopic maximum stresses for random fiber location variation and their probabilistic properties is required. For this analysis, the successive local approximation method is employed. The effectiveness of the approximate multiscale stochastic stress analysis has been discussed, while the square array is assumed in previous literature. For applicability confirmation of the method to evaluation of an actual problem, the usage of a hexagonal array model should be discussed. From these backgrounds, the above analysis with the hexagonal array model is performed, and validity and effectiveness of this approach are discussed with the numerical results.

Keywords

• multiscale stochastic stress analysis
• randomly arranged unidirectional fiber reinforced composite material
• successive local approximation
• hexagonal array model